Statistical circuit design with the use of a modified ellipsoidal technique

The ellipsoidal technique for design centering and feasible region approximation [1] is modified in this article. The feasible region is approximated by a hyperellipsoid determined by a sequence of decreasing volume, different shape, and center hyperellipsoids. The construction of the hyperplane cuts used for the generation of the sequence of the hyperellipsoids is modified to make use of the function values only. The hyperplane cuts are linearizations of the nonlinear constraints at proper boundary points. The choice of the nonlinear constraint to be linearized and the linearization point are optimized in order to obtain maximum reduction in the volume of the generated hyperellipsoid. This will speed up the convergence to the final hyperellipsoid. Practical examples to test the method are included and applications to centering, tolerancing, and yield estimation are also given. (C) 1997 John Wiley & Sons, Inc.